Terrestrial Radiation Budget Calculator

This is a single-layer energy balance for the whole planet. Incoming shortwave power is intercepted across Earth circular cross section and spread over the full sphere, which introduces the factor of four: with a solar constant of 1361 W/m2 and a planetary albedo of 0.30, the globally averaged absorbed flux is 1361 times 0.70 divided by 4, or about 238 W/m2. Setting outgoing longwave emission equal to that absorbed flux and inverting the Stefan-Boltzmann law with sigma equal to 5.670374419e-8 W/m2/K4 gives the equilibrium temperature. With emissivity set to 1.0 the result is the familiar bare-rock value of 255 K, or about minus 18 degrees C. The effective emissivity term is what converts that bare-rock number into something resembling the real surface. It is a lumped parameter, not a material property: a value near 0.612 reproduces the observed 288 K mean surface temperature and stands in for the atmosphere absorbing and re-emitting outgoing infrared radiation. Real land and ocean surfaces have thermal emissivities between 0.95 and 0.99, so this parameter should be read as a crude index of greenhouse opacity rather than a measured quantity. The albedo of 0.30 is itself a sum of roughly 20 percent from clouds and roughly 10 percent from surface and clear-sky scattering, and cloud response remains the largest single uncertainty in climate projections. The model has no latitude structure, no ocean heat uptake, and no feedbacks, so it cannot reproduce the observed top-of-atmosphere imbalance of roughly 0.7 to 1.0 W/m2 that CERES satellite instruments measure.

Joseph Fourier framed the problem in the 1820s, asking why Earth is warmer than a simple accounting of solar heating suggests and proposing that the atmosphere retards the escape of what he called dark heat. Claude Pouillet measured the solar flux in 1838, and John Tyndall demonstrated in 1859 laboratory work that water vapour and carbon dioxide absorb infrared radiation strongly while nitrogen and oxygen do not. The arithmetic only became possible after Josef Stefan 1879 fourth-power radiation law and Ludwig Boltzmann 1884 thermodynamic derivation. Svante Arrhenius used these pieces in 1896 to produce the first quantitative estimate of the surface warming from doubling atmospheric carbon dioxide. Twentieth century work turned the balance into a working climate tool. George Simpson studied radiative equilibrium of the atmosphere in the 1920s, and Syukuro Manabe and Richard Wetherald 1967 radiative-convective model showed that convective adjustment must accompany radiative transfer to give realistic profiles, work recognized with a share of the 2021 Nobel Prize in Physics. Mikhail Budyko and William Sellers independently published energy balance climate models in 1969 that added latitude and ice-albedo feedback to this same framework. Observational closure came from space: the Earth Radiation Budget Experiment flew from 1984, and the CERES instruments have measured top-of-atmosphere shortwave and longwave fluxes continuously since Terra launched in 1999, supporting the widely reproduced global energy budget diagrams published by Kevin Trenberth, John Fasullo and Jeffrey Kiehl in 2009.